enh(CPlusPlus): add functions to binary-search-tree (#318)

algorithms/CPlusPlus/Trees/binary-search-tree.cpp

@@ -1,4 +1,5 @@
 #include <iostream>
+#include <cmath>
 
 //Structure of the Tree
 struct TreeNode{
@@ -47,6 +48,120 @@ void Insert(TreeNode*& root, const int& data){
 	else 			    { Insert(root->left, data); }
 }
 
+
+bool isfull(TreeNode* root){
+        /**
+         *
+         * Check if a binary tree is full or not
+         * A binary tree is full when every node in the 
+         * tree has either two or zero child nodes.
+         *
+         * @params: `root` root/parent node of the tree
+         *
+         * @return: true if it the binary tree is full else false
+         */
+
+        if(root == nullptr)                                     { return true; }
+        if(root->left == nullptr && root->right == nullptr)     { return true; }
+        if((root->left != nullptr && root->right != nullptr) )  { return isfull(root->left) && isfull(root->right); }
+        return false;
+}
+
+int depth(TreeNode* root){
+        /**
+         * Find the depth of the left most tree.
+         * Here the depth of the left most tree is found but 
+         * it is only a matter of preference.
+         *
+         * @params: `root` root/parent node of the tree
+         *
+         * @return: `d` returns the depth of the left most tree
+         */
+
+        int d = 0;
+        while(root != nullptr){
+                root = root->left;
+                d++;
+        }
+        return d;
+}
+
+
+bool perfect_recursive(TreeNode* cur, int depth, int level = 0){
+        /**
+         * A Recursive strategy to check if a tree is perfect or not
+         *
+         * A binary tree is perfect if when all the inner node's
+         * has two children and the all the leaf node's are at the
+         * same level.
+         *
+         * @params: `cur`  node of the tree
+         * @params: `depth` depth of the left most tree
+         * @params: `level` level of the cur node
+         *
+         * @return: true if the binary tree is perfect else false
+         */
+
+        if(cur == nullptr)                                { return true; }
+        if(cur->left == nullptr && cur->right == nullptr) { return depth == level; }
+        if(cur->left != nullptr && cur->right != nullptr) {
+                return perfect_recursive(cur->left, depth, level+1) && perfect_recursive(cur->right, depth, level+1);
+        }
+	return false;
+}
+
+int count_nodes(TreeNode* cur){
+        /**
+         * Count the number of node's in the tree
+         * @params: `cur`  node of the tree
+         */
+
+        if(cur != nullptr){ return 1 + count_nodes(cur->left) + count_nodes(cur->right); }
+	return 0;
+}
+
+
+int height(TreeNode* cur){
+        /**
+         * Find the height of the tree
+         *
+         * @params: `cur`  node of the tree
+         */
+
+        if(cur != nullptr){ return 1 + std::max(height(cur->left),  height(cur->right)); }
+	return 0;
+}
+
+bool perfect(TreeNode* cur){
+        /**
+         * Knowing the height and the number of node's of
+         * the tree we can find whether the tree is perfect or not
+         *
+         * A binary tree is perfect if when all the inner node's
+         * has two children and the all the leaf node's are at the
+         * same level.
+         */
+
+        int h = height(cur) - 1;
+        int N = count_nodes(cur);
+        if(N == pow(2, h+1) - 1) { return true; }
+        return false;
+}
+
+bool isperfect(TreeNode* root){
+        /**
+         *
+         * @params: `root` root/parent node of the tree
+         *
+         * @return: true if the binary tree is perfect else false
+         */
+
+        //if(perfect(root))                           { return true; }
+        if(perfect_recursive(root, depth(root) - 1)) { return true; }
+	return false;
+}
+
+
 void print(TreeNode* root){
 	/**
 	 * Print the tree in an inorder fashion
@@ -78,21 +193,31 @@ void free(TreeNode* root){
 
 int main(){
 	TreeNode* root = nullptr;
+
 	Insert(root, 37);
 	Insert(root, 19);
 	Insert(root, 4);
-	Insert(root, 2);
-	Insert(root, 11);
 	Insert(root, 22);
-	Insert(root, 20);
 	Insert(root, 51);
 	Insert(root, 55);
 	Insert(root, 42);
+	Insert(root, 20);
+	Insert(root, 11);
+	Insert(root, 2);
 	
 	print(root);
+
+	TreeNode* n = find(root, 19);
+	std::cout << "\nValue of n: " << n->data << std::endl;
+
+	if(isfull(root)) { std::cout << "The binary tree is FULL" << std::endl; }
+	else 		{ std::cout << "The binary tree is not FULL" << std::endl; }
+
+	if(isperfect(root)) { std::cout << "The binary tree is PERFECT" << std::endl; }
+	else 		   { std::cout << "The binary tree is not PERFECT" << std::endl; }
+
 	/* 
 	Tree structure
-
 		37
 	       /  \
 	      19  51
@@ -101,12 +226,13 @@ int main(){
 	   /\	/ 	
 	  2 11  20
 
-	  Output: 2 4 11 19 20 22 37 42 51 55
-
+	OUTPUT:
+	  2 4 11 19 20 22 37 42 51 55
+	  Value of n: 19
+	  The binary tree is not FULL
+	  The binary tree is not PERFECT
 	*/
-
-	TreeNode* n = find(root, 2);
-	std::cout << "\nValue of n: " << n->data << std::endl; //Output: Value of n: 2
+	
 
 	// free the memory
 	free(root);